Pre-distortion for fast power transient waveforms

ABSTRACT

An apparatus and a method select and use parameter values for an RF power amplifier linearizer to pre-distort the input signals of a power amplifier, so as to achieve a linear output response in the power amplifier. The apparatus and the method select from a number sets of parameter values, each set of parameter values corresponding to a different output power range of the power amplifier. The set of parameters include a coefficient vector tailored for the particular output power range for that set. The power amplifier input power is repeatedly measured and filtered at various time intervals. The input power measurements may be filtered by a fast attack/slow decay filter, which follows the peaks of the measurements under operation of the fast attack portion of the filter and provides a low variance during operation of the slow decay portion of the filter. The coefficient values for the predistortion linearization of the power amplifier is adapted dynamically, in response to changes in the input power level of the power amplifier. In one embodiment, hysteresis is used to reduce the rate at which the predistortion linearizer hops between two sets of the parameter values. Using the apparatus and the method, good ACLR across a wide range of power amplifier output power is achieved. Such characteristics are particularly advantageous in a system in which waveforms having fast power transients are present.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to signal processing. In particular, thepresent invention relates to providing pre-distortion of input signalsto a power amplifier in order to linearize the output response of thepower amplifier, especially in the presence of fast power transientwaveforms.

2. Discussion of the Related Art

One design goal of a typical RF power amplifier linearizer is to providelow adjacent channel leakage ratio (ACLR) over a wide range of outputpower of the associated power amplifier. In the prior art, such an RFpower amplifier linearizer uses a single set of coefficients for alloperating power levels for the power amplifier. The set of coefficientsare, for example, the coefficients of corresponding basis functions inthe output response of the power amplifier linearizer, in which theoutput response is expressed as a linear sum of basis functions.However, using a single set of coefficients achieves good performance(i.e., within 1 dB of the best ACLR) typically only across a 1.5 dBrange of output powers. Thus, there is a need for improving ACLRperformance over a wider range of output powers.

SUMMARY OF THE INVENTION

The present invention provides, in an RF power amplifier linearizer, anapparatus and a method that select and use a set of parameter values,from multiple set of parameter values, to pre-distort the input signalsof the associated power amplifier, so as to achieve a linear outputresponse in the power amplifier.

According one embodiment of the present invention, multiple sets ofparameter values are maintained for an RF power amplifier linearizer,with each set of parameter values corresponding to a different outputpower range of the power amplifier. The parameters in each set ofparameter values include a coefficient vector. The values in thecoefficient vector for each set of parameter values are tailored for theparticular output power range corresponding to that set. In thatembodiment, the power amplifier input power is repeatedly measured andfiltered at various time intervals. The input power measurements arefiltered by a fast attack/slow decay filter, which tracks the peaks ofthe measurements under operation of the fast attack portion of thefilter and provides a low variance during operation of the slow decayportion of the filter. The values of the coefficient vector forpredistortion linearization of the power amplifier is adapteddynamically, in response to changes in the input power level of thepower amplifier. In one embodiment, hysteresis is used to reduce therate at which the predistortion linearizer hops between two sets of theparameter values. The present invention achieves good ACLR performanceacross a wide range of power amplifier output power and is able torespond quickly to rapid increases in the input power level of the poweramplifier. Such characteristics are particularly advantageous in asystem in which waveforms having fast power transients are present. Thepresent invention allows an RF power amplifier linearizer integratedcircuit to be tailored to any power amplifier that may be used in apower amplifier system.

The present invention is better understood upon consideration of thedetailed description below in conjunction with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows system 100 which is suitable for implementing an apparatusor a method of the present invention.

FIG. 2 is a block diagram showing the signal processing within the RFpower amplifier linearizer 1, in accordance with one embodiment of thepresent invention.

FIG. 3 shows parameter values used by controller 24, in accordance withone embodiment of the present invention.

FIG. 4 plots adjacent channel leakage ratio (ACLR) as a function ofrelative output power for a particular power amplifier.

FIG. 5 plots relative distortion power as a function of relative outputpower for a particular power amplifier.

FIG. 6 illustrates the performance of the fast attack/slow decay filteron a two-carrier waveform, in accordance with one embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 shows system 100 which is suitable for implementing an apparatusor a method of the present invention. System 100 includes signalcouplers 3, 7 and 5, RF power amplifier linearizer 1 and power amplifier2. When its input signal is at a high power, power amplifier 2 may gointo compression (i.e., the output signal gain of power amplifier 2 atthat high power is less than the output signal gain of power amplifier 2at a lower power). As shown in FIG. 1, signal coupler 3 provides inputwaveform 11 as input signal 4 to RF power amplifier linearizer 1. Inresponse to input signal 4, RF power amplifier linearizer 1 generatesoutput signal 8 which is coupled by signal coupler 7 to input waveform11 to provide input signal (PA_(IN)) 9 of power amplifier 2. When inputwaveform 11 has a power that falls within power amplifier 2's region ofcompression, output signal 8 of RF power amplifier linearizer 1increases the power of input signal 9. In this manner, couplers 3 and 7and the RF power amplifier linearizer 1 increase the power at the peaksof input signal 9, so as to compensate for power amplifier 2'scompression. Signal coupler 5 couples output signal 10 to provide afeedback signal (RF_(FB)) 6. Output waveform 12—a system output signalof system 100—is ideally simply a scaled version of the input waveform11. In other words, output signal 12 is maintained at a substantiallyconstant gain relative to input signal 11 (i.e., SYS_(OUT)(t)=GSYS_(IN)(t), where G is the system voltage gain).

FIG. 2 is a block diagram showing the signal processing within the RFpower amplifier linearizer 1, in accordance with one embodiment of thepresent invention. As shown in FIG. 2, input waveform 4 is representedby its complex envelope (x(t)) 14, which is provided by power splitter13 to power detector (PDET) 15, quadrature up-converter 23 and spectrumperformance monitor 26. Power detector 15 provides baseband signal(d(t)) 16, which represents the power in complex envelope x(t)) (i.e.,d(t)=G_(D)|x(t)|², where G_(D) is set by programmable detector gainsignal 28 from controller 24). From baseband signal 16 (i.e., d(t)),non-linear function generators 17 generates monomials of d(t) at variousamounts of delay. In one embodiment, the following monomials aregenerated:f ₁(t)=d(t)f ₂(t)=d ²(t)f ₃(t)=d ³(t)f ₄(t)=d(t−τ)f ₅(t)=d ²(t−τ)f ₆(t)=d ³(t−τ)f ₇(t)=d(t−3τ)f ₈(t)=d ²(t−3τ)f ₉(t)=d ³(t−3τ)f ₁₀(t)=d(t−5τ)f ₁₁(t)=d ²(t−5τ)f ₁₂(t)=d ³(t−5τ)where τ may be, for example, 1 ns.

The monomials are used as basis functions (f_(k)(t)) 18 to constructin-phase baseband correction signal (s_(i)(t)) 22 b and quadraturebaseband correction signal (s_(r)(t)) 22 a. Basis functions 18 are eachmultiplied at multiplying digital-to-analog converters (DACs) 20 by acorresponding one of coefficients 19 and summed, at summers 21 a and 21b, to provide in-phase baseband correction signal 22 a and quadraturebaseband correction signal 22 b. Quadrature up-converter 23 mixes thebaseband corrections signals 22 a and 22 b with complex envelope 14 toprovide output signal (RF_(OUT)) 8. In one example, all of coefficients19 are zero, except for the first one (w_(1,1)), which is given byw_(1,1)=0.3, so that in-phase baseband correction signal 22 a is givenby s_(i)(t)=0.3 G_(D)|x(t)|² and quadrature baseband correction signal22 b is given by s_(r)(t)=0. Consequently, the complex envelope of theoutput signal 8 of quadrature up-converter 23 is given by:RF_(OUT)(t)=0.3 G_(D)|x(t)|²x(t). In this example, in-phase basebandcorrection signal 22 a is a third order distortion signal with anamplitude governed by the w_(1,1) coefficient. If power amplifier 2 hasa third order compression characteristic (e.g.,PA_(OUT)(t)=[1−0.3|PA_(IN)(t)|²]PA_(IN)(t)), and there are no carrierphase delays, then the w_(1,1) coefficient compensates for thecompression characteristic until system 100, as shown in FIG. 1, has anoutput distortion that is minimized. Output signal 12 thus approximatesa linear system: SYS_(OUT)(t)≈G SYS_(IN)(t).

As shown in FIG. 1, any distortion that is introduced into poweramplifier 2's output waveform 10 is sampled by coupler 5 in RF feedbacksignal 6. As shown in FIG. 2, spectrum analysis is performed in spectrumperformance monitor 27 on RF feedback signal 6 to measure out-of-band(OOB) distortion power 32. In one embodiment, input waveform 4 containstwo tones at RF frequencies f₁ and f₂ and power amplifier 2 has a strongthird order distortion. As a result, intermodulation products appear atRF frequencies 2f₁−f₂ and 2f₂−f₁ so that RF_(FB) spectrum performancemonitor 27 measures power at RF frequencies that include 2f₁−f₂ and2f₂−f₁ Coefficients 19 are adapted by controller 24 to minimizeout-of-band distortion power 32. When measuring out-of-band distortionpower 32, controller 24 selects a gain in spectrum performance monitor27, represented by RF_(FB) Gain signal 31, that provides a low noisefigure but does not clip the analog-to-digital converter within RF_(FB)spectrum performance monitor 27.

Controller 24 sets to a constant (i.e., not time-varying) level a gainfor RF_(IN) spectrum performance monitor 26. This gain, which isrepresented in FIG. 2 by RF_(IN) gain signal 29, enables RF_(IN)spectrum performance monitor 26 to provide RF_(IN) power signal 30across the operating power range of input signal (RF_(IN)) 4. RF_(IN)power signal 30 is preferably measured as frequently as possible toallows controller 24 to quickly react to changes in the signal level ofinput waveform (RF_(IN)) 4. The actual measurement frequency in eachcase depends, for example, on the capabilities of RF_(IN) spectrumperformance monitor 26 and controller 24. In practice, if themeasurement interval is set too short, the measured RF_(IN) power signal30 will have too much variance. If the measurement interval is set toolong, the delay between the time input signal (RF_(IN)) 4 actuallychanges in power and the time at which controller 24 actually changesdetector gain signal 28 and coefficients 19 will be too long. Duringsuch a delay, detector gain signal 28 and coefficients 19 may not be attheir optimum values and the resulting distortion in system outputsignal 12 may be too high. In one embodiment of the present invention,the measurement interval is set to 40 μs and a new measurement iscomputed every 110 μs.

Controller 24 may be implemented by a microprocessor that executes afirmware program. FIG. 3 shows parameter values used by controller 24,in accordance with one embodiment of the present invention. As shown inFIG. 3, the parameter values are organized into 7 sets (“bins”)according to the power of input signal (RF_(IN)) 4. provided in column42 Each bin, which is assigned a bin number (shown in column 41 of FIG.3). is associated with a range of power levels R_(n), 0≦n<7, centered ata value defined relative to a working point R (see, column 42). Forexample, bin 0 (which has the lowest power) is centered at power levelR₀=R+1.50, bin 2 is centered at power level R₂=R (i.e., the workingpoint), and bin 6 (which has the highest power) is centered at powerlevel R₀=R−3.00. The number of bins and the location of the workingpoint shown in FIG. 3 are merely exemplary. The actual number of binsprovided and the placement of the working point are design parameters,and many other values for these parameters are possible. One may selectas the working point of a power amplifier, for example, the ratio of the3 dB peak compression power to the peak-to-average power ratio (PAR) ofthe input waveform. Typically, the peak power is defined as that powerlevel threshold which is exceeded by the instantaneous power 0.01% ofthe time. Other definitions of peak power may also be devised and used.Associated with each bin also are, for example, the power detector gain(i.e., the value represented by detector gain signal 28) in column 43,RF_(FB) spectrum power performance monitor gain (i.e., the valuerepresented in RF_(FB) gain signal 31) in column 44, and coefficient 19in column 45. The linearized power amplifier output power is provided incolumn 46, where WP denotes the power at the working point.

Controller 24 repeatedly reads the value on RF_(IN) power signal 30 fromRF_(IN) spectrum performance monitor 26 and applies the power readingsto a “fast attack/slow decay” filter, described below. The output of thefast attack/slow decay filter is used to select the bin to use, based onmatching the filter output with FIG. 3's power levels of column 42.Based on the selected bin number, the power detector gain is selectedfrom column 43 and downloaded to power detector 15 through detector gainsignal 28. In a similar fashion, coefficients 19 are selected fromcolumn 45 and downloaded to the multiplying DACs 20. To maximize thedynamic range of RF_(FB) spectrum performance monitor 27, the RF_(FB)gain for the selected bin in column 44 is downloaded via RF_(FB) gainsignal 31 to RF_(FB) spectrum performance monitor 27. The power detectorgains in column 43 and the RF_(FB) gains in column 44 may be provided inunits of dB, as shown in FIG. 3, but other convenient units are alsopossible. In a similar fashion, the power units in FIG. 3 are providedas dBm, but other units such as mW, dBFS (dB relative to full scale ofan analog to digital converter), dBN (a scale based on log₂: e.g.,dBN=0.3322 dBFS+18), or s16 (a scale based on using 16 bit arithmetic:e.g., s16=340.1654 dBFS+18431) may also be used. Parameter values may berepresented in any suitable way. For example, a tabular listing of thegains, a binary encoding of the gains in which each bit representswhether or not an attenuator is used or bypassed, or a control word fora variable gain amplifier may also be used.

The motivation behind using multiple sets of parameter values, one setfor each selected bin (or range of power levels), is illustrated by FIG.4. FIG. 4 plots adjacent channel leakage ratio (ACLR) as a function ofrelative output power for a particular power amplifier. ACLR is ameasure of out-of-band distortion¹. As used in this detaileddescription, ACLR may be provided by: ACLR=D−S, where D is thedistortion power and S is the signal power (both in dB). In FIG. 4, thex-axis is the difference in dB between the power amplifier output powerand the working point of the power amplifier. In FIG. 4, the coefficientvector w₄ is trained at an output power of WP−1.5 dB (bin 4 of FIG. 3),The coefficient vector is then held constant and the ACLR is measured asthe power amplifier output power was varied from WP−8.8 dB to WP+5.5 dB.As seen in FIG. 4, the best ACLR performance occurs at WP−1.5 dB, thepower at which the coefficient vector is trained. The same training maybe carried out at different output power levels. In one embodiment, theACLR curves as a function of relative output power at different powerlevels form a family of curves similar to that corresponding tocoefficient vector w₄ shown in FIG. 4, but offset horizontally by thedifferent output power ranges. In each curve, the local minimum ACLRcorresponds to the power amplifier output power associated with thecenter of the bin. This result suggests that, to have good ACLRperformance, a system should have several different coefficient vectorsto be applied at different output power ranges. For a definition ofACLR, please see paragraph 6.5.2.2.1 of ETSI TS 125 141, “UniversalMobile Telecommunications System (UMTS); Base Station (BS) conformancetesting (FDD) (3GPP TS 25.141 version 9.2.0 Release 9)”, February 2010.

FIG. 5 plots relative distortion power as a function of relative outputpower for a particular power amplifier. The relative distortion power ofFIG. 5 is given by D−D_(WP), where D_(WP) is the distortion power whenthe power amplifier is operating at its working point. In the embodimentillustrated in FIG. 5, the slope of the relative distortion power curveat the working point is 8:1, such that, near the working point, forevery dB that the signal's power is increased, the distortion powerincreases 8 dB. Although each given power amplifier has a differentdistortion versus power curve, in this embodiment, the power amplifierwas within 1 dB of the best relative distortion across a 1.5 dB range,from WP−2.6 dB to WP−1.1 dB. Consequently, to ensure that the relativedistortion power suffer no more than 1 dB decrease in performance, thebin spacing should be less than 1.5 dB.

The bin spacing shown in FIG. 3 is 0.75 dB, although other bin spacingsmay also be used (e.g., non-uniform spacings). If the bin spacing is settoo large, then the stitching together of the family of curves, one foreach bin (e.g., the ACLR curve of FIG. 4), would have large scallops andthe average ACLR would degrade. If the fast attack/slow decay filteroutput, described below, has a high standard deviation relative to thebin spacing, then the pre-distortion operation may switch between binsmore frequently than is desirable, as momentary degradation in ACLRperformance may result during bin switching. Consequently, anyunnecessary switching should be avoided. In the embodiment shown in FIG.3, seven bins with a 0.75 bin spacing span 4.5 dB, from the first bincenter to the last bin center. If the bin spacing is increased, thedynamic range over which the power amplifier can be linearized is alsoincreased. If the number of bins is increased, then the memoryrequirements to hold the various hardware parameter values, includingcoefficients 19, is also increased. As shown in FIG. 5, as the poweramplifier output power decreases, the relative distortion power alsodecreases, such that, below some output power level (e.g., 1 dB belowthe working point), the relative distortion power may be sufficientlylow that additional bins are not warranted. This characteristic limitsthe required number of bins, the required bin spacing or both.

EVDO, HSDPA, WiMax, LTE, and TD-SCDMA are wireless communicationstandards that are known to generate fast power transients (FPT) duringoperation. A FPT waveform hops between power levels, remaining at eachlevel only for a short period of time. For example, in one multi-carrierwaveform, EVDO traffic on one carrier exists simultaneously with CDMAtraffic on a second carrier. When both carriers have active datatraffic, performance degradations due to fast power transients are notsignificant. However, when the EVDO carrier is not transmitting data,signal pulses are generated for 182 μs to transmit the medium accesscontrol (MAC) and pilot overhead, but data traffic for the EVDO carrieris turned off for 651 μs, as there is no data in the payload. As aresult, the power of the multi-carrier waveform hops between two powerlevels, one level corresponding to when activities are present in boththe EVDO carrier and the CDMA carrier, and the other corresponding towhen activities are present only in the CDMA carrier.

An FPT waveform may result in significant performance degradation in alinearization system that has only one coefficient vector. As seen inFIG. 6, the FPT waveform may hop between two power levels: WP−1.5 dB andWP. In the example of FIG. 5, the relative distortion power is 10 dBgreater when the power is at WP, as compared to when the relativedistortion power is at WP−1.5 dBm. The average distortion, D_(AVE), forthis single coefficient set scenario, can be expressed as:

$D_{AVE} = {10\;{\log_{10}\left\lbrack {\int_{- \infty}^{\infty}{{p(S)}10^{\frac{D{(S)}}{10}}\ {\mathbb{d}S}}} \right\rbrack}}$where p(S), is a probability density function for the instantaneoussignal power, S, and D(S) is the relative distortion power associatedwith that signal power (i.e., the curve of FIG. 5). Thus, to minimizethe average distortion, the system should avoid operating where D(S) islarge or when 10^([D(S)/10]) is larger still. Better performance isachieved for the example of FIG. 5, by operating with the coefficientset w₂, which optimizes relative distortion power performance at a powerlevel of WP rather than operating with the coefficient set w₄, whichoptimizes the relative distortion power at a power level of WP−1.5 dB.By using the coefficient set near WP, one avoids the steep portion ofthe curve near WP in the curve of FIG. 5. To first order, the relativedistortion power versus relative output power curve for coefficientvector w₄ has the same form as the relative distortion power versusrelative output power curve corresponding to the coefficient vector w₂,except that it is shifted to the right by 1.5 dB.

To operate in the presence of FPT waveforms, it is desirable to moverapidly into operation at the higher power level during the high powerportions of the FPT waveform. At the same time, however, one should alsoavoid excessively switching back and forth between adjacent bins. A lowpass filter on the RF_(IN) power measurement signal 30 provides a lowvariance relative to the bin spacing, so that controller 24 infrequentlyswitches between bins. Rapid acquisition during high power operation andlow variance are desirable and may be achieved using a fast attack/slowdecay filter. The fast attack/slow decay filter may be implemented, forexample, in the firmware of controller 24. Other implementations of thefast attack/slow decay in hardware are also possible.

Let x(n) represent the sequence of the input signal derived fromsampling RF_(IN) power measurement signal 30. The units of sequence x(n)may be the s16 format previously discussed. In the embodiment discussedabove, sequence x(n) is provided as the input sequence to a fastattack/slow decay filter and sequence y(n) is the sequence obtained asthe output sequence of the filter. Internal to the filter, thedifference between the current input sample of x(n) and the previousoutput sample of y(n) is computed:d(n)=x(n)−y(n−1)This difference is used to select the filter characteristic of the fastattack/slow decay filter. Specifically, if the difference is positive,then the fast attack filter coefficient β_(A) is used, otherwise a slowdecay filter coefficient β_(D) is used:

${v(n)} = \left\{ \begin{matrix}{2^{- E_{A}}{d(n)}} & {{{if}\mspace{14mu}{d(n)}} \geq 0} \\{2^{- E_{D}}{d(n)}} & {otherwise}\end{matrix} \right.$where v(n) is an internal filter variable representing a scaleddifference, E_(A) is the filter exponent for fast attack, β_(A)=2^(−E)^(A) is the filter coefficient for fast attack, E_(D) is the filterexponent for slow decay, and β_(D)=2^(−E) ^(D) is the filter coefficientfor slow decay. This form for v(n) allows v(n) be computed using only anarithmetic right shift. The filter output y(n) is updated using theprevious output y(n−1) adjusted by the scaled difference v(n):y(n)=y(n−1)+v(n)If E_(A)=0, then v(n)=d(n) without delay and y(n)=x(n) during the fastattack condition, i.e., the filter output immediately is set to thefilter input if the input sample x(n) is greater than or equal to theprevious filter output, y(n−1). The z-transform of the filter's impulseresponse during the slow decay is:

$\frac{Y(z)}{X(x)} = \frac{\beta_{D}}{1 - {\left( {1 - \beta_{D}} \right)z^{- 1}}}$which shows that the fast attack/slow decay has a first order low-passfilter characteristic.

FIG. 6 illustrates the performance of the fast attack/slow decay filteron a two-carrier waveform, in accordance with one embodiment of thepresent invention. In FIG. 6, the first carrier contains EVDO traffic in25% of the slots over a period of time. The power of the carrier havingEVDO traffic is also 2.5 dB stronger (when the traffic was present) thanthe power of the second carrier which carries CDMA traffic. Thus, theattack filter coefficient β_(A) has an exponent E_(A)=0, and the decayfilter coefficient β_(D) has an exponent E_(D)=9. As shown in FIG. 6,when both carriers are present, the input power to the fast attack/slowdecay filter input (as shown by the thin line in FIG. 6) isapproximately −8.4 dBFS and when only the CDMA carrier was present, theinput power of the filter is approximately −12.8 dBFS. The output signalof the fast attack/slow decay filter tracks the peaks of the filterinput as shown by the thick line in FIG. 6. The standard deviation ofthe filter output is 0.09 dB which is significantly smaller than the binstep size of 0.75 dB. Consequently the fast attack/slow decay filtertracks the peaks of RF_(IN) power signal 30 rapidly, while achieving alow variance so that bin switching occurs infrequently.

The fast attack/slow decay filter output, y(n), is compared against thepower levels in column 42 of FIG. 3 to select the bin to use. One methodselects the bin, indexed by k, according to the first instance that thefilter output y(n) is greater than a threshold placed half-way betweenadjacent bins:

${y(n)} \geq \frac{{R(k)} + {R\left( {k + 1} \right)}}{2}$as k varies from 0 to 5, otherwise the bin with the smallest power isselected (i.e., k=6). This method has the characteristic that, if thefilter output y(n) is close to the threshold and varies from measurementto measurement (e.g., as shown in FIG. 6), controller 24 will hopfrequently between two adjacent bins. As controller 24 loadscoefficients 19 into multiplying DACs 20, an instant in time may existat which some of the coefficients in the corresponding coefficientvector for one bin have been loaded, while the rest of the coefficientsin multiplying DACs 20 are those coefficients in the coefficient vectorfor the previous bin. This partially loaded condition may cause theout-of-band distortion to temporarily increase until the full set ofcoefficients has been loaded. Consequently, the rate at which controller24 hops between two adjacent bins should be reduced, when possible. Thismay be achieved by making the current bin, k(n), for processing epochn+1 artificially larger than its neighbors. Hysteresis causes thecurrent bin to be greedier than the other bins. One method for choosingthe new bin, k(n+1), for the processing epoch n+1, selects that binwhich minimizes the distance between the filter output and the center ofthe bin, but with the current bin's distance reduced by the hysteresisfactor, H:

$\min\limits_{k{({n + 1})}}\left\{ \frac{{{y(n)} - {R\left\lbrack {k\left( {n + 1} \right)} \right\rbrack}}}{1 + {H\;{\delta\left\lbrack {{k\left( {n + 1} \right)} - {k(n)}} \right\rbrack}}} \right\}$where H=0.5 typically (i.e., the current bin is 50% larger than theother bins), and the delta function is given by:

${\delta(m)} = \left\{ \begin{matrix}1 & {{{if}\mspace{14mu} m} = 0} \\0 & {otherwise}\end{matrix} \right.$

To process epoch n, controller 24 compares the currently selected binnumber k(n) with the bin number from the previous processing epochk(n−1), and if they are different, then controller 24 loads the D_(k(n))value for power detector gain signal 28 from column 43 of FIG. 3 intothe power detector 15, the S_(k(n)) value for RF_(FB) SPM gain signal 31from column 44 of FIG. 3 into the RF_(FB) Spectrum Performance Monitor27 from, and coefficients 19 (w_(k(n))) from column 45 of FIG. 3 intothe multiplying DACs 20. If bin number k(n) is the same as k(n+1), thenno change is made for processing epoch n+1. RF power amplifierlinearizer 1 takes a measurement, typically 40 μs in duration using theRF_(IN) spectrum performance monitor 26 to produce the RF_(IN) powersignal 30 which in turn serves as input to the fast attack/slow decayinput sample x(n). The output of the filter is y(n) for processing epochn. y(n) is then used to select the bin number k(n+1), for the nextprocessing epoch n+1. If bin number k(n) is the same as k(n+1) and x(n)also falls in the range of bin k(n), then the epoch n+1 qualifies foradaptation and the coefficients w_(k(n+1)) are adapted. The coefficientvector for bin k is only adapted when the power level falls within therange of bin k.

In one embodiment, coefficients 19 are selected from multiplecoefficient vectors, each vector corresponding to a bin centered at aselected power level. Adaptation of coefficients 19 in that embodimentuses a modified simultaneous perturbation stochastic approximation(SPSA) algorithm² on each coefficient vector. The modification is aquadratic curve fit to the samples of the objective function. Adaptationof a coefficient vector is carried out over several cycles, each cycletaking three qualified processing epochs, which need not be consecutive.For each cycle, a random perturbation vector p is generated that issmall in amplitude relative to coefficient vector and usually has fewnon-zero elements. A left coefficient vector u_(k)(−1)=w_(k)−p is loadedinto multiplying DACs 20 for the first qualified epoch of a cycle. Acenter coefficient vector u_(k)(0)=w_(k) is loaded for the secondqualified epoch of the cycle. A right coefficient vectoru_(k)(+1)=w_(k)+p is loaded for the third qualified epoch of the cycle.For these processing epochs, the corresponding values b(−1), b(0) andb(+1) of out-of-band distortion signal 32 is measured. A quadraticpolynomial is then fitted to these out-of-band distortion values and ifthe second derivative of the quadratic polynomial is positive andnon-zero, then the quadratic polynomial's minimum b(t) is found,otherwise the index of the least of the three distortion powers (i.e.,

$\left. {\min\limits_{t}\left\{ {b(t)} \right\}} \right)$is selected. James Spall, http://www.jhuapl.edu/SPSA/See also U.S. Pat.No. 7,026,873 “LMS-based adaptive pre-distortion for enhanced poweramplifier efficiency”

The amplitude of the perturbation is constrained to be interpolation(i.e., −1≦t≦1) rather than extrapolation. At the end of the cycle, anupdated coefficient vector for bin k is then computed using w_(k)

w_(k)+tp to achieve a smaller out-of-band distortion than the originalcoefficient vector. The coefficient vector for each bin is expected toconverge to a value which minimizes out-of-band distortion afteradaptation over a large number of cycles (e.g., several thousandcycles). At the onset, a large amplitude may be selected for theperturbation vector, so that the minimum is rapidly acquired;thereafter, the perturbation vector's amplitude may be reduced, so thatthe variance in out-of-band distortion may be reduced, and thecoefficient tracking time may be lengthened.

The above detailed description is provided to illustrate the specificembodiments of the present invention and is not intended to be limitingof the scope of the invention. Numerous variations and modificationwithin the scope of the invention are possible. The present invention isset forth in the following claims.

I claim:
 1. A linearizer for a power amplifier, comprising: a powerdetector which provides an instantaneous power signal based on an inputsignal to the linearizer; a function generator for generating a set ofbasis function signals based on the instantaneous power signal; a set ofdigital-to-analog converters which change amplitudes of the basisfunction signals in accordance with a set of corresponding coefficients;a signal generating circuit which provides an output signal of thelinearizer based on the changed amplitudes of the basis functionsignals; and a controller, which includes a filter sensitive to a changein the instantaneous power signal and which selects one of a pluralityof sets of parameter values based on an output of the filter, each setof parameter values corresponding to a range of signal power, and whichderives therefrom the set of corresponding coefficients for thedigital-to-analog converters.
 2. The linearizer of claim 1, wherein thecontroller further derives from the selected set of parameter values acontrol parameter value for the power detector.
 3. The linearizer ofclaim 1, wherein the power detector further comprises a spectrumperformance monitor, the controller further deriving from the selectedset of parameter values a control parameter value for the spectrumperformance monitor.
 4. The linearizer of claim 3, wherein the spectrumperformance monitor provides measurements of the input signal to thelinearizer in real time.
 5. The linearizer of claim 1, furthercomprising: a coupler for coupling an output signal of the poweramplifier as a feedback signal to the linearizer; and a spectrumperformance monitor which estimates an out-of-band distortion in thefeedback signal, wherein the controller derives from the selected set ofparameter values a control parameter value for the spectrum performancemonitor.
 6. The linearizer of claim 1, wherein the controller adapts theset of coefficients based on perturbation.
 7. The linearizer of claim 1,wherein the filter comprises a fast attack/slow decay filter.
 8. Thelinearizer of claim 1, wherein the filter tracks peaks in theinstantaneous power signal.
 9. The linearizer of claim 1, wherein thefilter responds more rapidly to an increase in an amplitude of theinstantaneous power signal than a decrease in the amplitude of theinstantaneous power signal.
 10. The linearizer of claim 1, wherein thecontroller applies to a hysteresis factor when selecting among the setsof parameter values, the hysteresis factor tends to disfavor a change inthe selected set of parameter values.
 11. The linearizer of claim 1,further comprising a coupler that sums the output signal of thelinearizer to the input signal to the linearizer to provide an inputsignal to the power amplifier.
 12. The linearizer of claim 1, whereinthe signal generating circuit comprises an in-phase summer and aquadrature summer, the in-phase summer and the quadrature summeroperating on the changed amplitudes of the basis function signals toprovide a complex baseband correction signal.
 13. The linearizer ofclaim 12, wherein the signal generating circuit further comprises aquadrature upconverter that mixes the complex baseband correction signalwith the input signal to the linearizer to form the output signal of thelinearizer.
 14. A method in a linearizer of a power amplifier,comprising: detecting an input signal to the linearizer to provide aninstantaneous power signal; generating a set of basis function signalsbased on the instantaneous power signal; providing a set ofdigital-to-analog converters which change the amplitudes of the basisfunction signals in accordance with a set of corresponding coefficients;based on the changed amplitudes of the basis function signals, providingas an output signal of the linearizer; and providing a controller, whichincludes a filter sensitive to a change in the instantaneous powersignal and which selects one of a plurality of sets of parameter valuesbased on an output of the filter, each set of parameter valuescorresponding to a range of signal power, and which derives therefromthe set of corresponding coefficients for the digital-to-analogconverters.
 15. The method of claim 14, wherein the controller furtherderives from the selected set of parameter values a control parametervalue for the power detector.
 16. The method of claim 14, whereinfurther comprises monitoring a spectrum performance in the input signalof the linearizer, the controller further deriving from the selected setof parameter values a control parameter value for controlling thespectrum performance monitoring.
 17. The method of claim 16, wherein thespectrum performance monitoring measures the input signal to thelinearizer in real time.
 18. The method of claim 14, further comprising:coupling an output signal of the power amplifier as a feedback signal tothe linearizer; and monitoring spectrum performance to estimate anout-of-band distortion in the feedback signal, wherein the controllerderives from the selected set of parameter values a control parametervalue for the spectrum performance monitoring.
 19. The method of claim14, wherein the controller adapts the set of coefficients based onperturbation.
 20. The method of claim 14, wherein the filter comprises afast attack/slow decay filter.
 21. The method of claim 14, furthercomprising tracking in the filter peaks in the instantaneous powersignal.
 22. The method of claim 14, wherein the filter responds morerapidly to an increase in an amplitude of the instantaneous power signalthan a decrease in the amplitude of the instantaneous power signal. 23.The method of claim 14, wherein the controller applies to a hysteresisfactor when selecting among the sets of parameter values, the hysteresisfactor tends to disfavor a change in the selected set of parametervalues.
 24. The method of claim 14, further comprising summing theoutput signal of the linearizer to the input signal to the linearizer toprovide an input signal to the power amplifier.
 25. The method of claim14, wherein providing the output signal of the linearizer comprisesproviding an in-phase summer and a quadrature summer, the in-phasesummer and the quadrature summer operating on the changed amplitudes ofthe basis function signals to provide a complex baseband correctionsignal.
 26. The method of claim 25, further comprising providing aquadrature upconverter that mixes the complex baseband correction signalwith the input signal to the linearizer to form the output signal of thelinearizer.